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Statistics & Data Science · pattern F, Dataset

One-way ANOVA from your mean squares.

Enter the between-group and within-group sums of squares with the group and sample counts for the F ratio, degrees of freedom and an interpretation against the critical value.

Inputs

The formula used

F = MS between ÷ MS within, where MS = SS ÷ df

Between-group degrees of freedom are k − 1 and within-group are N − k, where k is the number of groups and N the total number of observations.

F ratio

4.6792

df between
3
df within
36
MS between
413.3333
MS within
88.3333
Total sum of squares
4,420.00
Eta squared, effect size
0.2805
Decision against your critical value
reject the null — at least one group mean differs

A significant F says at least one group differs, not which. Post-hoc tests such as Tukey's are needed to identify the pairs, with their own correction for multiple comparisons.

Why not just run several t tests?

Comparing four groups pairwise needs six t tests, and at α = 0.05 the chance of at least one false positive rises to about 26%. ANOVA tests all groups at once with a single α, controlling that inflation. The price is that a significant result is non-specific: it tells you the group means are not all equal and leaves the question of which to a post-hoc procedure.

Questions about anova

What assumptions does ANOVA make?
Independent observations, approximately normal residuals and roughly equal variances across groups. Moderate departures are tolerable with equal group sizes; unequal sizes plus unequal variances is where it breaks.
What does eta squared tell me?
The proportion of total variance attributable to the group factor — the effect size. Report it alongside F, because a significant F on a large sample can accompany a trivial effect.
Which post-hoc test should I use?
Tukey's HSD for all pairwise comparisons with equal variances, Games–Howell where variances differ. Both correct for multiple comparisons; running plain t tests afterwards does not.

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Statistical output here is for coursework and learning. Reported p-values and intervals assume the conditions stated on the page; nothing here checks whether those conditions hold for your data.